Topological data analysis and diagnostics of compressible MHD turbulence

Abstract

The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with observations. One of the main challenges in this area is to identify robust \it{quantitative} measures to compare structures found in simulations with those inferred from astrophysical observations. A similar challenge is to compare quantitatively results from different simulations. Topological data analysis offers a range of techniques, including the Betti numbers and persistence diagrams, that can be used to facilitate such a comparison. After describing these tools, we first apply them to synthetic random fields and demonstrate that, when the data are standardized in a straightforward manner, some topological measures are insensitive to either large-scale trends or the resolution of the data. Focusing upon one particular astrophysical example, we apply topological data analysis to HI observations of the turbulent interstellar medium (ISM) in the Milky Way and to recent MHD simulations of the random, strongly compressible ISM. We stress that these topological techniques are generic and could be applied to any complex, multi-dimensional random field.

arXiv comment22 pages, 15 figures

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Cited by in corpus (4)

• Is the Observable Universe Consistent with the Cosmological Principle?
• Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals
• Homology reveals significant anisotropy in the cosmic microwave background
• More than a void? The detection and characterization of cavities in a simulated galaxy's interstellar medium